Question

Simplifique as expressoes:
A) √80+20-√45
____________=
√2

Answer 1

$\frac{\sqrt{80}+20-\sqrt{45}}{\sqrt{2}}\\\frac{\sqrt{2^4\cdot 5}+20-\sqrt{3^2\cdot 5}}{\sqrt{2}}\\\frac{4\sqrt{5}+20-3\sqrt{5}}{\sqrt{2}}\\\frac{\left(\sqrt{5}\cdot \left(4-3\right)\right)+20}{\sqrt{2}}\\\frac{\left(\sqrt{5}\cdot 1\right)+20}{\sqrt{2}}\\\frac{\sqrt{5}+20}{\sqrt{2}}\\\frac{\sqrt{5}+20}{\sqrt{2}}\cdot \frac{\sqrt{2}}{\sqrt{2}}\\\boxed{\bold{\frac{\sqrt{2}\cdot \left(\sqrt{5}+20\right)}{2}}}$